Research

I am currently working with David Aristoff and Olivier Pinaud. We study convergence rates and spectral properties of Bayesian sampling algorithms and Markov processes.

My recent publication with David Herzog, Gabriel Stoltz, and Maria Gordina establishes explicit rates of convergence for Langevin dynamics subject to singular potentials in a weighted norm.

More recently, with David Herzog, we have proven on the asymptotic behavior of degenerately stochastically forced Lorenz 96 systems.

My mathematical research and interests lie in:

  • Stochastic Processes

  • Chaos Theory and Nonlinear Dynamics

  • Functional Analysis

  • Partial Differential Equations

  • Quantum Mechanics

  • Mathematical Chemistry

A recent presentation of our Langevin dynamics results.

202103121101-Camrud.mp4

Research with Undergraduates

I was privileged enough to participate in mathematics research as an undergraduate at Concordia College, as well as through an NSF-funded research program at New York University. These experiences were invaluable to my future career as a mathematician, and I try to participate in leading undergraduate research whenever possible. The list of program topics I have led with undergraduates includes:

  • Fractals and iterated function systems

  • Sampling and interpolation theory

  • Markov chains and mixing times

  • Models for turbulent flow

  • Semigroup theory

  • Fractional operator theory